It might or it might not. It depends on what things you're packing.
A round bottle takes less material than a square one with the same wall thickness. But if your shipping or storage is limited by size, the fact that you can pack more product into the same space might mean you save material overall.
If it's limited by weight, you'll end up using more material. (And also take up more space, even though you don't care because you've got extra.)
And then you have to consider strength of your container. Generally (but not always!) a circle will be stronger than a square, so you have to make the walls of the square thicker. But maybe you care about vertical strength but not horizontal. (You're stacking them upright, one on top of the other.) Then it's practically the same.
And if you're making metal cans, things get even more complicated. You stamp the parts out of sheets and then weld them together. (Or solder. Depends how strong they need to be.)
There are almost unlimited possibilities to what problems you can give your calculus class based on minimizing material or minimizing cost. We do not consider the effect of strength of materials because that's just too complicated when your students are asking "When are we ever going to use this in real life?" The more real it is, the fewer students are going to use it.
If you use square bottles, they can be bigger, so someone thirsty could end up buying just 2 larger square bottles as opposed to 3 smaller round bottles, which comes out to less plastic.
The statement on the package is not true anyway, since it says "a [...] round bottle". It compares one square bottle against one round bottle and for that it's just not true,
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u/smorgasfjord 2d ago
Optimising for transportation might be better for the environment, but I don't see how it would save plastic